We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate K(i; j) = K’(i; j)∝ iujv at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with u + v ≤ 3and u ＜ 2 approaches a conventional scaling form, which reduces to the Smoluchovski form in the u = 1 case. On the other hand, for the system with u ＜ 2, the average aggregate size S(t) grows exponentially in the u + v = 3 case and as(t lnt)1/(5-2u) in another special case of v = u - 2. Moreover, this typical size S(t) grows as t1/(3 ) in the general u -- 2 ＜ v ＜ 3 - u case; while it always grows as t1/(5-2u) in the v ＜ u - 2 case.